IMAC 2022 - Characterizing Experimental Nonlinear Modal Coupling with 3D Surfaces - Moldenhauer
Nonlinearity is often encountered in structural dynamics, and while many system identification techniques have been explored, these existing approaches are ill equipped to properly address many nonlinear behaviors that are observed in practice. Although great progress has been made in developing methods for analyzing isolated nonlinear resonances, these methods typically assume that the modal properties are uncoupled, in that the response of one mode does not have any effect on the behavior of another. This is a suitable assumption when analyzing weakly nonlinear systems in which variations in the stiffness and damping of each mode can be accurately characterized as a univariate function of its response amplitude. However, this approach fails when the effects of modal coupling are no longer negligible, and individual modal properties vary with respect to multiple modal responses. To that end, this work explores a method for efficiently characterizing the coupling effects between two nonlinear resonances in terms of the relative modal response amplitude of each. This is done by simultaneously exciting the relevant structural modes at a variety of amplitude combinations and extracting amplitude dependent natural frequency and damping ratio curves for each mode from the response measurements. By representing each quasilinear modal parameter as a function of both modal amplitudes, a three-dimensional surface can then be formed that describes how each parameter changes as a function of coupling between the response amplitudes. In this paper, this approach is demonstrated utilizing experimentally measured nonlinear response data from a structure containing a large, jointed interface. Coupling behavior is observed by concurrently exciting pairs of modes of the structure that each activate the joint nonlinearity. Representing the measured response data in terms of the three-dimensional modal coupling surface offers an intuitive and concise means of characterizing and visualizing this complex nonlinear structural behavior.
Presented at IMAC 2022 in Orlando, Florida